Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class EdA {
	static long[] mods = {1000000007, 998244353, 1000000009};
	static long mod = mods[0];
	public static MyScanner sc;
    public static PrintWriter out;
	public static void main(String[] havish) throws Exception{
		// TODO Auto-generated method stub
 		sc = new MyScanner();
 		out = new PrintWriter(System.out);
 		int n = sc.nextInt();
 		int[] arr = readArrayInt1(n);
 		int sum = 0;
 		for(int j = 1;j<=n;j++){
 			sum+=arr[j];
 		}
 		int minval = Integer.MAX_VALUE;
 		int minindex = -1;
 		int maxval = Integer.MIN_VALUE;
 		int maxindex = -1;
 		int csmin = Integer.MAX_VALUE;
 		int csindex = -1;
 		int[] count = new int[n+1];
 		for(int j = 1;j<=n;j++) {
 			int temp = arr[j];
 			int val =0 ;
 			while(temp%2 == 0) {
 				val++;
 				temp/=2;
 			}
 			count[j] = val;
 			if (val < minval) {
 				minval = val;
 				minindex = j;
 			}
 			if (val > maxval) {
 				maxval = val;
 				maxindex = j;
 			}
 			
 			int s = sum-val;
 			int cs = 0;
 			while(s%2 == 0) {
 				s/=2;
 				cs++;
 			}
 			if (cs < csmin) {
 				csmin = cs;
 				csindex = j;
 			}
 		}

 		boolean[][] knap = new boolean[200001][n+1];
 		knap[0][1] = true;
 		for(int j = 1;j<=n;j++){
 			knap[arr[1]][1] = true;
 		}
 		boolean flag = true;
 		for(int j = 2;j<=n;j++) {
 			for(int k = 0;k<=200000;k++) {
 				if (knap[k][j-1] && k+arr[j] <= 200000)
 					knap[k+arr[j]][j] = true;
 				if (knap[k][j-1])
 					knap[k][j] = true;
 				
 			}
 		}
 		boolean allequal = true;
 		for(int j = 2;j<=n;j++){
 			allequal = allequal && (count[j] == count[1]);
 		}
 		if (allequal && sum%2 == 0 && knap[sum/2][n]) {
 			out.println(1);
 			out.println(csindex);
 		}
 		else if (allequal) {
 			out.println(0);
 		} else if (sum%2 == 0 && knap[sum/2][n]) {
 			if (sum%2 == 0) {
	 			out.println(1);
	 			out.println(minindex);
 			}
 			else{
 				out.println(1);
 				out.println(maxindex);
 			}
 		}
 		else{
 			out.println(0);
 		}
 		
 		
	 		
 		out.close();
 	}
	public static void sort(int[] array){
		ArrayList<Integer> copy = new ArrayList<>();
		for (int i : array)
			copy.add(i);
		Collections.sort(copy);
		for(int i = 0;i<array.length;i++)
			array[i] = copy.get(i);
	}
	static String[] readArrayString(int n){
		String[] array = new String[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.next();
		return array;
	}
	static int[] readArrayInt(int n){
    	int[] array = new int[n];
    	for(int j = 0;j<n;j++)
    		array[j] = sc.nextInt();
    	return array;
    }
	static int[] readArrayInt1(int n){
		int[] array = new int[n+1];
		for(int j = 1;j<=n;j++){
			array[j] = sc.nextInt();
		}
		return array;
	}
	static long[] readArrayLong(int n){
		long[] array = new long[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextLong();
		return array;
	}
	static double[] readArrayDouble(int n){
		double[] array = new double[n];
		for(int j =0 ;j<n;j++)
			array[j] = sc.nextDouble();
		return array;
	}
	static int minIndex(int[] array){
		int minValue = Integer.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(long[] array){
		long minValue = Long.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static int minIndex(double[] array){
		double minValue = Double.MAX_VALUE;
		int minIndex = -1;
		for(int j = 0;j<array.length;j++){
			if (array[j] < minValue){
				minValue = array[j];
				minIndex = j;
			}
		}
		return minIndex;
	}
	static long power(long x, long y){
		if (y == 0)
			return 1;
		if (y%2 == 1)
			return (x*power(x, y-1))%mod;
		return power((x*x)%mod, y/2)%mod;
	}
	static void verdict(boolean a){
        out.println(a ? "YES" : "NO");
    }
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } 
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String nextLine() {
            String str = "";
            try{
                str = br.readLine();
            } 
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
    }	
}

//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is